{"id":317,"date":"2022-12-09T15:31:54","date_gmt":"2022-12-09T14:31:54","guid":{"rendered":"https:\/\/www.mines-stetienne.fr\/fayol\/?page_id=317"},"modified":"2022-12-09T15:31:55","modified_gmt":"2022-12-09T14:31:55","slug":"these-preparee-par-jean-charles-croix","status":"publish","type":"page","link":"https:\/\/www.mines-stetienne.fr\/fayol\/theses\/these-preparee-par-jean-charles-croix\/","title":{"rendered":"Th\u00e8se pr\u00e9par\u00e9e par Jean-Charles CROIX"},"content":{"rendered":"\n

|D\u00e9partement G\u00e9nie math\u00e9matique et industriel |<\/a>
| Projets<\/a>\u00a0|\u00a0<\/a>\u00c9quipe<\/a><\/em>\u00a0|\u00a0Publications<\/a>\u00a0|\u00a0Partenaires |<\/a><\/a><\/p>\n\n\n\n

Titre : <\/strong>A new decomposition of Gaussian random elements in Banach spaces with application to Bayesian inversion<\/p>\n\n\n\n

R\u00e9sum\u00e9 : <\/strong><\/p>\n\n\n\n

L\u2019inf\u00e9rence est une activit\u00e9 fondamentale en sciences et en ing\u00e9nierie: elle permet de confronter et d\u2019ajuster des mod\u00e8les th\u00e9oriques aux donn\u00e9es issues de l\u2019exp\u00e9rience. Ces mesures \u00e9tant finies par nature et les param\u00e8tres des mod\u00e8les souvent fonctionnels, il est n\u00e9cessaire de compenser cette perte d\u2019information par l\u2019ajout de contraintes externes au probl\u00e8me, via les m\u00e9thodes de r\u00e9gularisation. La solution ainsi associ\u00e9e satisfait alors un compromis entre d\u2019une part sa proximit\u00e9 aux donn\u00e9es, et d\u2019autre part une forme de r\u00e9gularit\u00e9.<\/p>\n\n\n\n

Depuis une quinzaine d\u2019ann\u00e9es, ces m\u00e9thodes int\u00e8grent un formalisme probabiliste, ce qui permet la prise en compte d\u2019incertitudes. La r\u00e9gularisation consiste alors \u00e0 choisir une mesure de probabilit\u00e9 sur les param\u00e8tres du mod\u00e8le, expliciter le lien entre donn\u00e9es et param\u00e8tres et d\u00e9duire une mise-\u00e0-jour de la mesure initiale. Cette probabilit\u00e9 a posteriori, permet alors de d\u00e9terminer un ensemble de param\u00e8tres compatibles avec les donn\u00e9es tout en pr\u00e9cisant leurs vraisemblances respectives, m\u00eame en dimension infinie.<\/p>\n\n\n\n

Dans le cadre de cette th\u00e8se, la question de l\u2019approximation de tels probl\u00e8mes est abord\u00e9e. En effet, l\u2019utilisation de lois infini-dimensionnelles, bien que th\u00e9oriquement attrayante, n\u00e9cessite souvent une discr\u00e9tisation pour l\u2019extraction d\u2019information (calcul d\u2019estimateurs, \u00e9chantillonnage). Lorsque la mesure a priori est Gaussienne, la d’ecomposition de Karhunen-Lo\u00e8ve est une r\u00e9ponse \u00e0 cette question. Le r\u00e9sultat principal de cette th\u00e8se est sa g \u0301en \u0301eralisation aux espaces de Banach, beaucoup plus naturels et moins restrictifs que les espaces de Hilbert. Les autres travaux d\u00e9velopp\u00e9s concernent son utilisation dans des applications avec donn\u00e9es r\u00e9elles.<\/p>\n\n\n\n

Financeur :<\/strong><\/p>\n\n\n\n

Soutenance pr\u00e9vue :<\/strong> Octobre 2018<\/p>\n\n\n\n

Mots cl\u00e9s :<\/strong><\/p>\n\n\n\n

Directeurs de th\u00e8se :<\/strong><\/p>\n\n\n\n

Co-encadrement :<\/strong><\/p>\n\n\n\n

|D\u00e9partement G\u00e9nie math\u00e9matique et industriel |<\/a>
| Projets<\/a>\u00a0|\u00a0<\/a>\u00c9quipe<\/a><\/em>\u00a0|\u00a0Publications<\/a>\u00a0|\u00a0Partenaires |<\/a><\/a><\/p>\n\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

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